The essential problem obstructing the calculation of decay
amplitude is how to properly evaluate the hadronic matrix
elements of the local operators.
Using the Brodsky-Lepage approach [1]},
the hadronic matrix elements can be written as the
convolution of a hard-scattering kernels containing
perturbative QCD contributions with the universal
wave functions reflecting the nonperturbative dynamics.
Currently, there are three popular phenomenological
approaches to evaluate the hadronic matrix elements
as an expansion in the strong coupling constant
\({\alpha }_{s}\)  and in the ratio \({\Lambda }_{\rm QCD}/m_{Q}\) ,
which are entitled to
QCD factorization (QCDF) [2]},
the soft-collinear effective theory (SCET) [3]},
and the pQCD approach [4]}.
These methods differ from each other in several
aspects. For example, only the collinear degrees of
freedom are taken into account in QCDF and SCET,
while the transverse momenta implemented with the
help of the Sudakov formalism in pQCD approach.
The other different features of these methods are
power counting, the choice of the scale at which
the strong interaction effects are calculated,
how to deal with the contribution of spectator
scattering and weak annihilation, and so on.
With the running LHCb and the advent of SuperKEKB
physics program, the precision of observables will
be greatly improved, and it should be possible to
disentangle the underlying dynamics in nonleptonic
\(B\)  decays.
